Details

sample162.0ms

Algorithm

intervals

Results

35.0ms	70×	body	5120	valid
23.0ms	394×	body	80	nan
19.0ms	53×	body	2560	valid
16.0ms	209×	body	80	valid
9.0ms	17×	body	10240	exit
7.0ms	23×	body	1280	valid
4.0ms	17×	body	640	valid
2.0ms	9×	body	320	valid
0.0ms	1×	body	160	valid

simplify109.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	60	26
1	304	25
2	3462	25
3	5003	25
done	5003	25

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 58.6b

localize21.0ms

Local error

Found 4 expressions with local error:

17.9b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
17.9b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
17.9b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
24.5b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite767.0ms

Algorithm

rewrite-expression-head

Rules

211×	`add-exp-log` `add-cbrt-cube`
117×	`prod-exp` `cbrt-unprod`
45×	`cbrt-undiv` `div-exp`
7×	`*-un-lft-identity`
6×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def`
4×	`pow1` `expm1-log1p-u` `times-frac` `log1p-expm1-u` `div-inv`
3×	`frac-2neg` `clear-num` `associate-/r` `associate-/l`
2×	`sqrt-div` `frac-add`
1×	`+-commutative` `flip3--` `flip3-+` `sum-log` `flip--` `flip-+` `distribute-lft-out`

Counts

4 → 156

Calls

4 calls:

43.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
43.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
43.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
626.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series559.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
99.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
99.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
261.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify124.0ms

Counts

168 → 168

Iterations

Useful iterations: 2 (106.0ms)

Iter	Nodes	Cost
0	594	2246
1	3877	1589
2	5001	1584
done	5001	1584

prune375.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 36.3b

localize5.0ms

Local error

Found 1 expressions with local error:

6.4b	(* (/ c0 (* 2.0 w)) 0)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log` `add-cbrt-cube`
7×	`associate-l`
6×	`add-sqr-sqrt`
4×	`add-cube-cbrt` `*-un-lft-identity` `prod-exp` `cbrt-unprod`
3×	`pow1` `times-frac` `associate-r`
2×	`cbrt-undiv` `div-exp`
1×	`expm1-log1p-u` `mul0` `pow-prod-down` `associate-l/` `-commutative` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`

Counts

1 → 30

Calls

1 calls:

25.0ms

(* (/ c0 (* 2.0 w)) 0)

series2.0ms

Counts

1 → 3

Calls

1 calls:

1.0ms

(* (/ c0 (* 2.0 w)) 0)

simplify286.0ms

Counts

33 → 33

Iterations

Useful iterations: 2 (282.0ms)

Iter	Nodes	Cost
0	178	40
1	1861	24
2	5001	14
done	5001	14

prune72.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 34.8b

localize2.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune14.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 34.8b

localize30.0ms

Local error

Found 4 expressions with local error:

17.9b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
17.9b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
24.5b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
24.5b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

142×	`add-exp-log` `add-cbrt-cube`
78×	`prod-exp` `cbrt-unprod`
30×	`cbrt-undiv` `div-exp`
10×	`fma-def` `*-un-lft-identity`
8×	`add-log-exp`
6×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `expm1-log1p-u` `times-frac` `sqrt-div` `frac-add` `log1p-expm1-u` `div-inv`
2×	`+-commutative` `flip3--` `frac-2neg` `flip3-+` `clear-num` `associate-/r` `sum-log` `flip--` `flip-+` `distribute-lft-out` `associate-/l`

Counts

4 → 132

Calls

4 calls:

43.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
43.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
621.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
624.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series717.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
99.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
260.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
259.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify127.0ms

Counts

144 → 144

Iterations

Useful iterations: 2 (105.0ms)

Iter	Nodes	Cost
0	594	2392
1	3877	1858
2	5001	1848
done	5001	1848

prune461.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 34.8b

regimes280.0ms

Accuracy

0% (2.5b remaining)

Error of 34.4b against oracle of 31.9b and baseline of 34.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2	0
1	2	0
done	2	0

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.0s	2212×	body	5120	valid
779.0ms	12997×	body	80	nan
663.0ms	1747×	body	2560	valid
416.0ms	6774×	body	80	valid
284.0ms	565×	body	10240	exit
257.0ms	862×	body	1280	valid
100.0ms	421×	body	640	valid
41.0ms	238×	body	320	valid
17.0ms	142×	body	160	valid